Implementation method for rapid scalar multiplication algorithm in elliptic curve cryptosystem

Abstract

The invention discloses an implementation method for a rapid scalar multiplication algorithm in an elliptic curve cryptosystem. The method at least comprises a scalar multiplication algorithm procedure of binary coding with the minimum Hamming weight and provided with symbols from left to right, and the method comprises the following steps of: arranging definitions on a finite prime number field, being arbitrary point, and being arbitrary integer; inputting'':''; outputting'':''; A. commanding '', ,''; B. decreasing progressively until, implementing: a. commanding; b. '', ,''; c. if, commanding; C. returning. The implementation method for the rapid scalar multiplication algorithm in the elliptic curve cryptosystem provided by the invention, the binary coding with the minimum Hamming weight and provided with the symbols from left to right is applied to the rapid scalar multiplication algorithm in the elliptic curve cryptosystem, a novel binary coding scalar multiplication algorithm with the symbols is created, which can be faster achieved. The novel binary coding scalar multiplication algorithm has the advantages that: arithmetic speed is high, additional memory plint space and coordinate change are not needed during calculation, calculation period is reduced, and the like.

Description

technical field [0001] The invention relates to a method for realizing a fast point product algorithm in an elliptic curve cryptosystem. Background technique [0002] The elliptic curve cryptosystem (ECC) proposed by Victor Miller and Neal Koblitz in 1985 applied elliptic curves to cryptography and became an important branch of public key cryptography. Its main advantages are small key size, fast implementation speed and security Relatively high, because ECC has the same security strength, it can use less overhead, such as: calculation amount, storage amount, bandwidth, software and hardware implementation scale, etc., so it is especially suitable for computing power and integrated circuit space limited, Bandwidth is limited, high-speed implementation is required, etc. [0003] Although the elliptic curve cryptosystem has many advantages mentioned above, it has not completely replaced other public key cryptosystems at present, and its implementation speed is restricted. The...

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Problems solved by technology

[0003] Although the elliptic curve cryptosystem has many advantages mentioned above, it has not completely replaced other public key cryptosystems at present, and its implementation speed is restricted. Therefore, the research on the encryption and decryption speed of the elliptic curve cryptosystem has become a hot spot. The point multiplication operation is the basic operation to realize the elliptic curve cryptosystem, and it is also the most time-consuming operation. Its operation efficiency directly determines the performance of ECC. It needs additional space for storing points, coordinate changes are required during the operation process, the number of calculation cycles is large, and the calculation speed is slow.

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